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I'm trying to get my head around the following problem, any help is appreciated. My maths skills aren't the best, so apologies in advanced for its stupidity.

Say I'm in a car, and I'm driving directly towards a stationary car (Car A) at 5 meters per second. Every second I get 5 meters closer to Car A, obviously.

Now, say there's another stationary car behind me (Car B) to the right at a 45 degree angle. Every second I measure my distance to Car B, as well.

My rate of change to Car A is consistent at 5 meters per second, yet, correct me if I'm wrong, my rate of change to Car B varies from second to second. For every second measured, my distance to Car B has changed by a different increment, as compared to the previous measurement. It's not a smooth change, second by second.

Why is this? What is it about the angles that causes my rate of change to Car A to be consistent, but my rate of change to Car B to differ?

Many thanks for any clarification,

Steven

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  • $\begingroup$ Use the fact that the distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. $\endgroup$ – Hussain-Alqatari Sep 15 '19 at 13:09
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Think how you measuring angle. Now Cars are travelling in 2 D dimension (Since cars don't fly) angle $$tan \theta = \frac{y-distance-difference}{x -distance -difference}$$. Assume your car (say P) starts by origin and car A at some where at Y axis and car B is on $y=tan({\pi \over 4}) .x$ . Now you if you see after some time x distance is constant from car P to A and it is zero , that's why angle is constant and it is also zero. but if you see both distances from car B are changing.

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